Overland Flow Modeling with the Shallow Water Equations Using a Well-Balanced Numerical Scheme: Better Predictions or Just More Complexity

Abstract

International audienceIn the last decades, several physically based hydrological modeling approaches of various complexities have been developed that solve shallow water equations or their approximations using various numerical methods. Users of the model may not necessarily know the different hypotheses underlying these development and simplifications, and it might therefore be difficult to judge if a code is well adapted to their objectives and test case configurations. This paper aims to compare the predictive abilities of different models and evaluate potential gain by using an advanced numerical scheme for modeling runoff. Four different codes are presented, each based on either shallow water or kinematic wave equations, and using either the finite volume or finite difference method. These four numerical codes are compared with different test cases, allowing to emphasize their main strengths and weaknesses. Results show that, for relatively simple configurations, kinematic wave equations solved with the finite volume method represent an interesting option. Nevertheless, as it appears to be limited in case of discontinuous topography or strong spatial heterogeneities, for these cases they advise the use of shallow water equations solved with the finite volume method

An efficient and stable hydrodynamic model with novel source term discretization schemes for overland flow and flood simulations

“…In practice, implicit discretization is often reformulated to derive an effective explicit scheme. Considering a 1‐D problem, many schemes [e.g., Song et al ., ; Busaman et al ., ; Cea and Blade , ; Cea and Vazquez‐Cendon , ; Burguete et al ., ; Liang et al ., ; Costabile et al ., ; Singh et al ., ; Rousseau et al ., ] adopt the following discretized equations where q x = hu is the unit discharge in the x direction, F is the momentum flux term, S bx is the bed slope term, and is the time step. For the implicit scheme as described in (13) and (14), the local acceleration (flux) term becomes small and negligible when the friction term is predominant.…”

“…In practice, implicit discretization is often reformulated to derive an effective explicit scheme. Considering a 1-D problem, many schemes [e.g., Song et al, 2011a;Busaman et al, 2015;Cea and Blade, 2015;Cea and Vazquez-Cendon, 2010;Burguete et al, 2008;Liang et al, 2006;Costabile et al, 2013;Singh et al, 2015;Rousseau et al, 2015] adopt the following discretized equationŝ…”

Determinants of modelling choices for 1-D free-surface flow and morphodynamics in hydrology and hydraulics: a review

“…When the full Saint-Venant equations are not needed or impossible to apply due to calculation time, an option is to neglect one or several terms of the momentum equation (Ponce and Simons, 1977;Romanowicz et al, 1988;Moussa andBocquillon, 1996a, 2000;Rousseau et al, 2015). In most practical applications for flood routing, the unsteadiness (i) and convective acceleration (ii) terms in Eq.…”

A new efficient implicit scheme for discretising the stiff friction terms in the shallow water equations

“…To provide stable simulations, implicit schemes have been widely used to discretise the friction source terms (e.g. Fiedler and Ramirez, 2000;Liang et al, 2007;Cea et al, 2010;Song et al, 2011;Costabile et al, 2013;Simons et al, 2014;Busaman et al, 2015;Cea and Blade, 2015;Rousseau et al, 2015;Singh et al, 2015 ). Unlike the explicit schemes, implicit schemes use the velocities at the new time step to evaluate the friction terms.…”

“…Other researchers (e.g. Liang et al, 2007;Cea et al, 2010;Song et al, 2011;Costabile et al, 2013;Busaman et al, 2015;Cea and Blade, 2015;Rousseau et al, 2015;Singh et al, 2015 ) express the friction terms as the product of the velocity in the current time step and that in the new time step to obtain an explicit formula. Although these schemes may effectively avoid the numerical instability caused by the stiff friction terms, they commonly relax the flows to a wrong steady state, which may consequently lead to incorrect simulation results ( Xia et al, 2017 ).…”